There exist numerous fields in which the determination of void rate is of interest and notably in fields as varied as the nuclear industry, the food-processing industry, the oil industry, the chemical industry, cryogenic applications, medicine (imaging and problems of decompression sickness) or else the field of underwater acoustics.
More precisely in the nuclear field, and notably for the fourth generation of fast neutron nuclear reactor (or “FBR” standing for “Fast Breeder Reactor”), the SFR (“Sodium Fast Reactor”) reactor appears very promising.
This family of reactors presents several challenges, in particular from the point of view of improving monitoring. Among the checks to be performed in the vessel of SFRs, there is one which was not taken into account within the framework of the development and exploitation of the Phenix and Superphenix SFRs: measurement of the continuous engassment of the primary sodium.
More precisely, “engassment” is defined as the presence of gas in a liquid (or a solid) in the form of bubbles (free gas). The gases dissolved in the liquid phase are not considered as belonging to the gas volume but as belonging to the liquid volume, when evaluating a so-called void rate.
Generally, an “FBR” is a reactor whose core is not moderated. Fast spectrum operation presents a certain number of advantages such as the possibility of implementing supergeneration or transmutation of minor actinides but it requires the use of a heat-exchanging fluid with low neutron capture cross-section such as liquid sodium. FIG. 1 illustrates the diagram of such a type of reactor according to the known art.
Indeed, liquid sodium possesses the properties expected of a heat-exchanging fluid, namely good thermal properties, low noxiousness, low cost etc. Its main drawbacks are its reactivity to air and especially to water and its opacity which renders the inspectability of the reactors more difficult than in water.
The gas present in free form in the liquid sodium of SFRs can have diverse origins and be of diverse kinds. There exist two possible sites of existence of gas bubbles in the sodium: the primary circuit (the main vessel in which the core is immersed) and the secondary circuit (circuit of the exchangers).
SFR type reactors use liquid sodium as heat-exchanging fluid. This fluid phase, present in the primary vessel of the reactor, circulates through the core, the pumps and the exchangers so as to extract the heat emanating from nuclear fission. This sodium pool is surmounted by a cover gas, also called a pile headspace (generally argon).
Ideally, this liquid sodium is perfectly pure and monophase. In reality, this is not the case: in addition to comprising a few impurities and dissolved gases, the sodium continuously comprises bubbles of free gas.
This continuous engassment nevertheless presents several negative consequences and notably the presence of bubbles in a liquid which very greatly modifies its acoustic properties (speed, attenuation, diffusion, nonlinear properties, etc.).
The deployment of acoustic measurement procedures for continuous monitoring, which is performed at the nominal power (measurement of the displacement of assembly heads, ultrasound thermometry based on flight time measurement), or the periodic checks operating in the shutdown regime (ultrasound telemetry, surface metrology, volume checking, etc.) requires a knowledge of an order of magnitude of the attenuation coefficients, so as to prove a priori that the amplitude of the signal is sufficient, as well as an order of magnitude of the lack of homogeneity of the spatial distribution, to prove that the speed calibrations carried out some distance from the effective measurement point, remain usable.
The aforementioned measurements thus necessarily demand a knowledge of the void rate value, backed up if appropriate with certain data relating to the histogram of the radii of the bubbles (at least the bounds).
If the evaluated void rate is not in itself directly deleterious in relation to the operation of the core, it is indirectly so if it participates in the generation of gas pockets at high points of the submerged structures.
The characterization of the continuous primary engassment in a reactor can thus serve as input data for trials or calculations for the formation and relaxation of these gas pockets. It must be pointed out that the abrupt relaxation of accumulated pockets of gas formed part of the scenarios envisaged for explaining the series of emergency shutdowns on reactors that has operated in the past.
Moreover, the continuous tracking of the engassment rate seems necessary for controlling the non-exceeding of several thresholds and notably:                the neutronic perturbation threshold (a priori too high to be attainable under the normal operating conditions of the reactor: of the order of several percent);        the blinding threshold of the systems for measuring activity in the pile headspace.        
Currently, in order to determine void rates, optical techniques are usable in translucent liquids, but these are no longer transposable into opaque media such as liquid sodium.
Linear acoustic techniques based on the attenuation or the spreading of an acoustic wave are usable but exhibit an ambiguity—between resonant bubble and big bubble—which is impossible to resolve without a priori knowledge about the bubble cloud. For certain ranges of void rate and of bubble sizes, speed measurements are sometimes implemented to determine the void rate.
In this context and to address the problematic issue of determining void rate applicable in a gas/liquid biphase non-translucent medium and notably of possibly very low void rate, typically of the order of 10−6 to 10−8, the present invention proposes to exploit the so-called “NRUS” procedure, frequently encountered in the literature under the acronym standing for “Nonlinear Resonant Ultrasound Spectroscopy”. It is a nonlinear acoustics technique used mainly in the field of the acoustics of solids.
Generally, a mechanical system possesses resonant modes, all associated with a natural resonant frequency. As a general rule, these resonant frequencies are dependent on the geometric characteristics and the speed of the waves in the medium constituting the system. Now, the speed in a medium is dependent on its density and its compressibility. In the case of nonlinear acoustics, the modulus of elasticity is not constant and is dependent on the applied stress. It follows from this that the resonant frequency of a nonlinear mechanical system varies as a function of the applied stress and therefore of the acoustic excitation amplitude.
Nonlinear resonant ultrasound spectroscopy consists in observing this type of phenomenon by exciting the mechanical system considered while performing a frequency scan at various amplitudes. A shift between the resonance peaks then appears.
The authors K. Van Den Abeele et al. have notably proposed in the article, “On the quasi-analytic treatment of hysteretic nonlinear response in elastic wave propagation”—J. Acoust. Soc. Am. 101 (4), April 1997 1885-1898, the following model of the nonlinear modulus of elasticity:
      K    ⁡          (              ɛ        ,                              ∂            ɛ                                ∂            t                              )        =            K      0        ⁡          [              1        +        βɛ        +                  α          ⁡                      (                          Δɛ              +                                                sign                  ⁡                                      (                                                                  ∂                        ɛ                                                                    ∂                        t                                                              )                                                  ⁢                ɛ                                      )                              ]      With β the conventional nonlinear parameter and α the nonconventional nonlinear parameter, ε being the instantaneous strain and Δε the amplitude of the strain.
If f0 is the linear resonant frequency of a mechanical system (measured at low amplitudes) and f the resonant frequency measured for waves of larger amplitude and by considering the parameter α to be strongly predominant over the parameter β, this seeming to be confirmed by the experiments described in the articles by K. Van Den Abeele et al.—Nonlinear ElasticWave Spectroscopy (NEWS) Techniques to Discern Material Damage, Part I: Nonlinear Wave Modulation Spectroscopy (NWMS), Part II: Single Mode Nonlinear Resonance Acoustic Spectroscopy—Res Nondestr Eval (2000) 12: 17-42 or Micro-damage diagnostics using nonlinear elastic wave spectroscopy (NEWS)—NDT&E International 34 (2001) 239-248, the following relation is obtained:
                    f        0            -      f              f      0        ≈  αΔɛ
The NRUS procedure consists in measuring a frequency shift which turns out to be proportional to the nonconventional nonlinear parameter by frequency scanning. The frequency shift observed is a fast dynamics phenomenon.
The field of nonlinear elasticity of materials and notably of materials such as rocks has already been explored for a long time, but the technique today called NRUS began to be studied in depth and exploited for the characterization of media really toward the middle of the 1990s.
An NRUS procedure for characterizing damage to materials has notably been described in U.S. Pat. No. 6,330,827. This patent entails applying the NRUS procedure and deducing, from the frequency shift, damage to the material tested.
The article by M. Muller et al.—Nonlinear resonant ultrasound spectroscopy (NRUS) applied to damage assesment in bone—J. Acous. Soc. Am., Vol. 118(6), p. 3946-3952, December. 2005, presents another interesting application of the NRUS technique: the detection of fractures in bones. Spectroscopy of a healthy bone exhibits a constancy of the resonant frequency whereas a fractured bone exhibits a frequency shift.
The use of the RNUS procedure for detecting defects in materials has also been described in the article by Payan et al.: “Applying nonlinear resonant ultrasound spectroscopy to improving thermal damage assessment in concrete”, 13 Mar. 2007.
Thus, according to the known art, the procedures of NRUS type are employed to detect defects constituting discontinuities which are the source of nonlinearities in solid media.
Concerning biphase media, the inventors have mentioned in a publication: Cavaro M. ET AL: “Towards in-service acoustic characterization of gaseous microbubbles applied to liquid sodium” 2009 1ST INTERNATIONAL CONFERENCE ON ADVANCEMENTS IN NUCLEAR INSTRUMENTATION MEASUREMENTS METHODS AND THEIR APPLICATIONS” XP031704404, the possibility of using acoustic nonlinearities notably to detect bubble sizes by virtue of the presence of two acoustic wave transducers emitting in a biphase medium, a first transducer emitting an acoustic wave at a fixed first frequency f1, a second transducer emitting an acoustic wave at a variable second frequency f2. The bubbles present in the bubbly medium generate an acoustic wave with a frequency difference Δ(f1−f2) detected by a hydrophone, frequency scanning thus making it possible to detect various frequency differences and thus various sizes of bubble.
In this article, the authors mention the possibility of using the procedure of RNUS type but without proposing any solution making it possible to implement such a procedure and to do so in order to determine a void rate in a biphase medium.